mlsanityData to 7 Oct 2026

Riemannian Local Mechanism for SPD Neural Networks

arXiv 2201.10145 ↗First posted 25 Jan 2022cs.CVcited by 22

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Abstract (arXiv)

The Symmetric Positive Definite (SPD) matrices have received wide attention for data representation in many scientific areas. Although there are many different attempts to develop effective deep architectures for data processing on the Riemannian manifold of SPD matrices, very few solutions explicitly mine the local geometrical information in deep SPD feature representations. Given the great success of local mechanisms in Euclidean methods, we argue that it is of utmost importance to ensure the preservation of local geometric information in the SPD networks. We first analyse the convolution operator commonly used for capturing local information in Euclidean deep networks from the perspective of a higher level of abstraction afforded by category theory. Based on this analysis, we define the local information in the SPD manifold and design a multi-scale submanifold block for mining local geometry. Experiments involving multiple visual tasks validate the effectiveness of our approach. The supplement and source code can be found in https://github.com/GitZH-Chen/MSNet.git.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 20 of its 53 references that are in the map. First posted on arXiv 25 Jan 2022.

Builds on

20 of 53 references.

References · 20

  1. 2014Going Deeper with Convolutionscited by 4,231
  2. 2018DARTS: Differentiable Architecture Searchcited by 1,782
  3. 2019Res2Net: A New Multi-scale Backbone Architecturecited by 468
  4. 2016Convolutional Two-Stream Network Fusion for Video Action Recognitioncited by 384
  5. 2017First-Person Hand Action Benchmark with RGB-D Videos and 3D Hand Pose Annotationscited by 229
  6. 2016A Riemannian Network for SPD Matrix Learningcited by 162
  7. 2019H+O: Unified Egocentric Recognition of 3D Hand-Object Poses and Interactionscited by 139
  8. 2019Fair DARTS: Eliminating Unfair Advantages in Differentiable Architecture Searchcited by 129
  9. 2017Interpretable 3D Human Action Analysis with Temporal Convolutional Networkscited by 88
  10. 2019Riemannian batch normalization for SPD neural networkscited by 72
  11. 2016Building Deep Networks on Grassmann Manifoldscited by 58
  12. 2016Dimensionality Reduction on SPD Manifolds: The Emergence of Geometry-Aware Methodscited by 29
8 more
  1. 2021GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognitioncited by 27
  2. 2016Transition Forests: Learning Discriminative Temporal Transitions for Action Recognition and Detectioncited by 18
  3. 2018A Statistical Recurrent Model on the Manifold of Symmetric Positive Definite Matricescited by 18
  4. 2019Dilated Convolutional Neural Networks for Sequential Manifold-valued Datacited by 11
  5. 2013Sparse Coding and Dictionary Learning for Symmetric Positive Definite Matrices: A Kernel Approachcited by 9
  6. 2020ManifoldNorm: Extending normalizations on Riemannian Manifoldscited by 8
  7. 2020Neural Architecture Search of SPD Manifold Networkscited by 6
  8. 2018Multiple Manifolds Metric Learning with Application to Image Set Classificationcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 4; 2025: 4; 2026: 9.

22 papers.

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  1. 2023Adaptive Log-Euclidean Metrics for SPD Matrix Learningcited by 13
  2. 2023SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric Positive Definite Spacecited by 13
  3. 2023Improving Expressivity of GNNs with Subgraph-specific Factor Embedded Normalizationcited by 12
  4. 2023Riemannian Multinomial Logistics Regression for SPD Neural Networkscited by 11
  5. 2024Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometrycited by 9
  6. 2024A Lie Group Approach to Riemannian Batch Normalizationcited by 8
  7. 2024RMLR: Extending Multinomial Logistic Regression into General Geometriescited by 8
  8. 2025Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometrycited by 7
  9. 2024Powerformer: A Section-adaptive Transformer for Power Flow Adjustmentcited by 5
  10. 2023Riemannian Self-Attention Mechanism for SPD Networkscited by 4
  11. 2025DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responsescited by 2
  12. 2026High-Resolution Underwater Camouflaged Object Detection: GBU-UCOD Dataset and Topology-Aware and Frequency-Decoupled Networkscited by 1
10 more
  1. 2025Riemannian Complex Hermit Positive Definite Convolution Network for Polarimetric SAR Image Classificationcited by 0
  2. 2025Learning Topology-Driven Multi-Subspace Fusion for Grassmannian Deep Networkcited by 0
  3. 2026RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphscited by 0
  4. 2026K-GMRF: Kinetic Gauss-Markov Random Field for First-Principles Covariance Tracking on Lie Groupscited by 0
  5. 2026ReManNet: A Riemannian Manifold Network for Monocular 3D Lane Detectioncited by 0
  6. 2026Riemannian Networks over Full-Rank Correlation Matricescited by 0
  7. 2026A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decodingcited by 0
  8. 2026Towards Robust EEG Decoding Based on Riemannian Self-Attentioncited by 0
  9. 2026LieBN: Batch Normalization over Lie Groupscited by 0
  10. 2026Geometric Feature Learning for Functional Data Valued on the Symmetric Positive Definite Manifoldcited by 0